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In a parallelogram OABC , it is given OA = a , OC = c , PB = 1/3AB and BQ = 1/3 BC . OQ and AB are extended to meet at S while CB abd OP are extended to meet at R
Express (a) BS in terms of c
(b) BR in terms of a

In a parallelogram OABC , it is given OA = a , OC = c , PB = 1/3AB and BQ = 1/3 BC . OQ and AB are extended to meet at S while CB abd OP are extended to meet at R
Express (a) BS in terms of c
(b) BR in terms of a

------------------------------------------(c) Show that RS is parallel to AC

angle RBS = angle CBA ...........vertical angles

BR/CB = BS/AB
(a/2)/a = (c/2)/c
1/2 = 1/2
True

Hence, triangle RBS is similar to triangle CBA.
And so, angle ACB = angle SRB
Therefore, RS is parallell to AC .....with RC as the transversal line, a pair of their alternate interior angles are congruent.